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When Spain played Belgium in the preliminary round of the men's hockey competition in the 2008 Olympics, the final score was 4 - 2.
Can you find all the possible half time scores for this match?
This challenge invites pupils to develop a systematic way of working and offers the opportunity for discussion in pairs, small groups and the whole class. For some learners, having a 'real' context might provide motivation to solve the problem.
Of course, you may wish to introduce this problem in the context of the scores of a local event, rather than the Olympics. This may help many pupils engage in the solving of the problem.
You could ask "If there are $24$ possible different half time scores, what could the final score have been?".
Some pupils may prefer to start with games where there are fewer goals, for example, 0 - 1, 1 - 0, 1 - 1 etc so that there are fewer possible half time scores.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?